发表机构
Centrum Wiskunde & Informatica; Delft University of Technology; Eindhoven University of Technology（荷兰国家数学与计算机科学研究所; 代尔夫特理工大学; 埃因霍温理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出观测插值框架，将预训练生成模型转化为无需重训的后验采样器，统一随机与确定性采样，并在高维动力学中验证。
AI 中文摘要
贝叶斯数据同化将模型预报与含噪观测相结合，但对高维、非高斯后验分布进行采样仍具挑战。我们提出一个观测插值框架，可将预训练的随机插值、流匹配和扩散模型转化为后验采样器，无需重新训练。将插值路径以观测为条件，可对漂移或速度产生共享的似然分数校正，从而统一随机与确定性后验采样。当中间似然分数已知时，所得随机微分方程和常微分方程可精确采样后验分布。为实用计算，我们使用闭式高斯替代来近似该分数，其均值经偏差校正，协方差由模型的源协方差膨胀。无雅可比和集成共享近似使该方法在高维中可行。我们在线性高斯动力学、随机二维纳维-斯托克斯方程以及自由度高达$O(10^4)$的城市气流上评估该框架。
英文摘要
Bayesian data assimilation combines model forecasts with noisy observations, but sampling high-dimensional, non-Gaussian posteriors remains challenging. We introduce an observation-interpolant framework that turns pretrained stochastic interpolant, flow matching, and diffusion models into posterior samplers without retraining. Conditioning the interpolant path on observations yields a shared likelihood-score correction to the drift or velocity, unifying stochastic and deterministic posterior sampling. The resulting SDEs and ODEs sample the exact posterior when the intermediate likelihood score is known. For practical computation, we approximate this score using a closed-form Gaussian surrogate with a bias-corrected mean and covariance inflated by the model's source covariance. Jacobian-free and ensemble-shared approximations make the method tractable in high dimensions. We evaluate the framework on linear-Gaussian dynamics, stochastic two-dimensional Navier-Stokes, and urban airflow with up to $O(10^4)$ degrees of freedom.
